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Hi Barry,</div>
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Following your instructions I implemented the matrix-free method to solve a large linear equation system resulted from a surface integration equation. The KSP solver works fine for single process, but it is problematic with multiple processes. The problem is
that each process only can access its own part of solution vector so that each process only conducts part of matrix-vector multiplication. MPI can be used to assemble these partial matrix-vector multiplication together. Does Petsc provide any ways to implement
multi-process matrix-free method? <br>
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Thanks,<br>
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Jiannan<br>
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<div id="divRplyFwdMsg" dir="ltr"><font face="Calibri, sans-serif" style="font-size:11pt" color="#000000"><b>From:</b> Barry Smith <bsmith@petsc.dev><br>
<b>Sent:</b> Tuesday, May 24, 2022 2:12 PM<br>
<b>To:</b> Tu, Jiannan <Jiannan_Tu@uml.edu><br>
<b>Cc:</b> petsc-users@mcs.anl.gov <petsc-users@mcs.anl.gov><br>
<b>Subject:</b> Re: [petsc-users] Using matrix-free with KSP</font>
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<div class="" style="word-wrap:break-word; line-break:after-white-space"><font color="red"><b>This e-mail originated from outside the UMass Lowell network.</b></font>
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You can use MatCreateMFFD <a href="https://urldefense.com/v3/__https://petsc.org/main/docs/manualpages/Mat/MatCreateMFFD/__;!!PVKG_VDCxu5g!stxq2NWGVjUihvHBQC9Rlk0aHVoowcy0PTQYMcQxQ4DqOEC05KSw6TmstSXKckiUgelHzy4ue-d10-zlXkw$" class="">https://petsc.org/main/docs/manualpages/Mat/MatCreateMFFD/</a>
MatMFFDSetFunction MatSetFromOptions MatMFFDSetBase and provide the matrix to KSP. Note you will need to use -pc_type none or provide your own custom preconditioner with <a href="https://urldefense.com/v3/__https://petsc.org/main/docs/manualpages/PC/PCSHELL/__;!!PVKG_VDCxu5g!stxq2NWGVjUihvHBQC9Rlk0aHVoowcy0PTQYMcQxQ4DqOEC05KSw6TmstSXKckiUgelHzy4ue-d1cA4fKGw$" class="">https://petsc.org/main/docs/manualpages/PC/PCSHELL/</a>
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<div class="">On May 24, 2022, at 1:21 PM, Tu, Jiannan <<a href="mailto:Jiannan_Tu@uml.edu" class="">Jiannan_Tu@uml.edu</a>> wrote:</div>
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I want to use a matrix-free matrix to solve a large linear equation system because the matrix is too large to be stored. Petsc user manual describes matrix-free method for SNES with examples. The matrix-free matrices section explains how to set up such a matrix,
but I can't find any example of matrix-free method with KSP. <span class="" style="background-color:rgb(255,255,255); display:inline!important">I am wondering how to apply the method to KSP iterative solver in parallel.</span></div>
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<span class="" style="background-color:rgb(255,255,255); display:inline!important"><span class="">I greatly appreciate your help for me to understand this topic. </span></span></div>
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<span class="" style="background-color:rgb(255,255,255); display:inline!important"><span class="">Jiannan Tu</span></span></div>
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